Based on the theoretical results from optimal control theory and sliding mode control, this paper proposes a discrete time nonlinear control law that guarantees the minimum time global stabilization of a chain of three integrators with bounded control input. Moreover, the proposed control law allows the minimum time trajectory tracking for a wide class of reference signals (such as step, ramp, saw tooth, etc.) and it can be used as nonlinear filter for the trajectories generation. (C) 2003 Elsevier Ltd. All rights reserved.